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We propose a kind of planar chiral optical metamaterial consisting of two layers of connected I-shape resonators arranged by a twist angle of 90°. Numerical simulation results demonstrate that our scheme can realize a mutual polarization conversion and dual-band asymmetric transmission for linearly polarized waves in the optical regime. For the forward propagation, the x-to-y and y-to-x polarization conversions in the proposed bilayered metamaterial result from the concentric and eccentric C-shaped dimers, respectively. The current distributions of bilayered metamaterials at the resonant frequencies are presented to interpret the dual-band asymmetric transmission. The polarization conversion efficiency and resonant frequencies can be modified via parametric study.
© 2014 Optical Society of America
1. Introduction
Chiral metamaterials that cannot be superimposed onto their mirror images exhibit many tantalizing electromagnetic properties such as negative refraction, giant optical activity and circular dichroism, and reciprocal directional-dependent asymmetric transmission. These chiral metamaterials have attracted lots of attention due to their flexible manipulation of wave polarizations [1, 2]. During the past several years, many kinds of metamaterials with symmetry-broken chiral structures have been used to manipulate wave polarization and achieve many customized functionalities and devices like circular and linear polarizers [3–7], polarization rotators [8, 9], polarization spectrum filters [10, 11] and handedness switching [12]. Optical activity is one of the most distinguished properties in artificial chiral metamaterials that was widely studied [13–20]. Importantly, giant optical activity was easily realized by electromagnetic field coupling in the bilayered chiral metamaterial [13]. Nowadays, the twisted-arc metamaterial has been proposed to achieve giant optical activity of about 76°/λ as well as giant circular dichroism of about 0.35 in the near-infrared regime [19], which is expected to enable various applications in modulation of light intensity and polarization in nanophotonic devices and integrated optics. Both optical activity and circular dichroism involved in 3D chiral media remain unchanged for two opposite directions, i.e. direction-independent. However, for metamateirals simultaneously having planar chirality (2D chirality) and anisotropy, a previously unknown phenomenon-asymmetric transmission (AT) was observed [21], which does not occurs in conventional 3D chiral metamaterials. The asymmetric transmission in planar chiral metamaterials is reciprocal and arises from polarization conversion dichroism, different polarization conversion efficiencies for the forward and backward propagation directions.
Since the asymmetric transmission was reported in planar chiral metamaterial [21], this phenomenon of linearly and circularly polarized waves in chiral metamaterials has been investigated both theoretically and experimentally from microwave to optical frequencies [22–37]. Although single-layer intrinsic and extrinsic chiral metamaterials can reveal asymmetric transmission [21–27], much more attention has paid to mutilayered chiral metamaterials for achieving high, multi-band asymmetric transmission [28–37], which are generally anisotropic. Asymmetric transmission in the chiral metamaterial is usually caused by the partial polarization conversion of the incident EM waves into one of the opposite polarization, which is asymmetric for the opposite directions of propagation [21], leading to a different total transmission for two opposite directions. A complete polarization conversion enables 100% asymmetric transmission, but this is hardly realized in single-layer chiral metamatieals [21–27]. Multilayered chiral metamaterials are usually stereo - the same structure but different spatial arrangements [38]. In most cases, the orthogonal arrangement has been introduced to enhance the coupling of two orthogonal modes and achieve high asymmetric transmission accompanied by low co-polarization transmission. Following the pioneering work of asymmetric transmissions of circularly polarized waves, a 3D low-symmetry metamaterial without any rotational symmetry showed 25% asymmetric transmission for linearly polarized light [29]. In theory, the criterion of realizing the asymmetric transmission only for linearly polarized waves has been presented [31]. Recently, it was theoretically found that asymmetric transmission for linear polarizations could be easily achieved by a monolayer of anisotropic chiral metamolecules through the constructive and destructive interferences between the contributions from anisotropy and chirality [27]. Several 3D metamaterials composed of twisted meta-molecules have been reported for having strong asymmetric transmission [33–37]. Combined with electromagnetic wave tunneling, a thin chiral metamaterial has been proposed to realize a dual-band asymmetric transmission of linearly polarized waves that was only suitable for single polarization [35]. Subsequently, dual-band asymmetric transmission and mutual polarization conversion were reported experimentally, individually for two orthogonal linearly polarized waves [36]. In the one band, an x-polarized wave can be completely converted to its cross-polarization while a y-polarized wave can be completely converted to its cross-polarization in the other band, distinct from the metamaterials previously reported that only showed an asymmetric transmission effect for single polarization. Mutual polarization conversion in optical frequencies is very attractive and offers an opportunity to manipulate polarization of light and realize novel devices like dual-band polarizer and filters. However, to our best knowledge, attempts have rarely been made to achieve mutual polarization conversion in optical frequencies. The operation of the asymmetric transmission phenomenon with mutual polarization conversion in simple structured metamaterials is still highly desirable.
In this work, we propose a kind of chiral metamaterials in optical frequencies that is composed of bilayered connected I-shape resonators in an orthogonal arrangement separated by a dielectric spacer layer. The proposed scheme can achieve mutual polarization conversion between two orthogonal linearly polarized waves. The simulated results show that the bilayered chiral metamaterial exhibits a dual-band asymmetric transmission and two orthogonal linearly polarized waves can direction-dependently pass through it in different bands, where a linearly polarized wave can be converted to its cross-polarization after transmission. The polarization conversion efficiency and resonant frequencies can be modified via parametric study. We believe that our approach can efficiently manipulate the polarization state of light.
2. Metamaterial structure
The bilayered metamaterials are geometrically identical, but are arranged with a twist angle of 90° in order to give birth to the strong chirality due to the near-field magnetic and electric coupling. Figure 1 illustrates our proposed chiral metamaterials. The unit cell is composed of an array of bilayered connected I-shape structures, separated by a dielectric spacer layer. The metallic layer on either side has the same pattern, but they are rotated with respect to each other by 90° around the z axis. In the simulation model, the dielectric layer is Si3N4 with a thickness of h = 30nm. The connected I-shape structure is gold with a thickness of t = 50nm. The other parameters are p = 400nm, l1 = 165nm, l2 = 150nm, l3 = 330nm, w = 50nm and b = 70nm. The unit cell of our proposed structure is square with a dimension of 400 × 400 nm2 shown in Fig. 1(c). The whole view of the metamaterial is shown in Fig. 1(d).
Fig. 1 Schematic of bilayered chiral metamaterial. (a) The view of the front layer. (b) The view of the back layer. (c) A unit cell in chiral metamaterial. (d) The whole view of a metamaterial.
We apply complex Jones matrices T matrix to analytically solve the polarization properties of the chiral metamaterials [29]. T matrix is the frequency-dependent Jones matrix, which describes the complex amplitudes of the incident to the transmitted field:
For convenience, we replaced Tij by A, B, C, D. The superscript f indicates the forward propagation (along the -z direction) and the subscript lin indicates the linear base. Then the transmission matrix for the propagation in the backward direction ( + z direction) can be expressed asThe asymmetric transmission of the linearly polarized waves is usually characterized by the parameter Δ, which is defined as the difference between the transmittances in two opposite propagation directions [29].It can be easily seen that the asymmetric transmission of y-polarized waves is opposite to that of x-polarized waves. Therefore, we can alternatively analyze the asymmetric transmission for x-polarized waves. An ideal asymmetric transmission should be that in one direction the transmission is unity while in the opposite direction the transmission is zero, thus the asymmetric transmission is also unity. This requires that two diagonal components (A and D) and one of the off-diagonal components (B or C) of the T matrix are nearly zero while the other off-diagonal component is unity [35, 36].3. Simulated results
We numerically demonstrate the mutual polarization conversion and dual-band asymmetric transmission of the bilayered optical metamterial by using the commercial simulation software, CST Microwave Studio. The dielectric constant of the spacer layer is set as 4.12 and gold is modeled by data from [39]. The periodic boundary condition is applied in the simulations. Here, the incident waves are x or y linearly polarized waves, propagating along the -z direction.
Figure 2 shows the simulated transmission for the forward propagation (the -z axis) in the frequency range of 150-300 THz, in which tij = |Tij|. The co-polarization transmission coefficient txx of x-polarized wave coincides well with tyy of y-polarized wave due to an orthogonal arrangement of two identical subwavelength resonators. In contrast to co-polarization transmission, the cross-polarization coefficient txy is extremely different from tyx at all frequencies we consider, indicating the presence of the AT effect for linearly polarized waves and the absence of the AT effect for circularly polarized waves [31]. Most interestedly, there are two individual pass bands showing strong polarization conversion in this metamaterial, one for x-to-y polarization conversion and the other for y-to-x polarization conversion. In Fig. 2(a), the cross-polarization transmission txy reaches a maximum of 0.5579 at around 203.8 THz and both the co-polarization transmission txx and tyy are about 0.4 while tyx is below 0.13. In this pass band, incident y-polarized wave is mostly transmitted to x-polarized wave while incident x-polarized wave is mostly blocked through the metamaterial slab. Meanwhile, an obvious resonant peak in tyx can be observed with a maximum larger than 0.5634 at around 259.8 THz and txx, tyy and txy are less than 0.1, indicating that incident x-polarized wave is almost completely transmitted to y-polarized wave while incident y-polarized wave cannot pass through the metamaterial slab. In addition, txy and tyx interchange with each other (not shown here) when the propagation direction is reversed.
Fig. 2 (a) Simulated transmission spectra of the metamaterial in forward propagation direction. (b) Simulated asymmetric transmission parameter Δx of the metamaterial corresponding to x-polarized wave in the forward propagation direction.
The asymmetric transmission effect of the linearly polarized waves is usually characterized by a parameter Δ, which is defined as the difference between the transmittances in two opposite propagation directions in Eq. (3). In order to clearly see the asymmetric transmission effect, Fig. 2(b) presents the simulated asymmetric transmission parameter Δ for forward propagating x-polarized waves. In particular, one can see that the asymmetry factor curves Δx shows two opposite peaks locating at about 203.8 and 259.8 THz. Two values of −0.29/0.32 in the curves Δx imply that the x/y -polarized wave in the forward direction is mostly forbidden/allowed at about 203.8 THz and allowed/forbidden at 259.8 THz, respectively. Obviously, mutual polarization conversion and dual-band asymmetric transmission can be achieved in our proposed metamaterial. To our knowledge, the asymmetric transmission parameter Δ is equivalent to that those previously reported in optical frequencies [29], but our dual-band asymmetric transmission corresponds to the x-to-y and y-to-x polarization conversion, respectively.
In terms of the circular transmission coefficient, the polarization state of the transmitted wave can be further studied. The circular transmission matrix can be calculated from the linear transmission matrix
where “+” and “–“ denote right-handed (RCP) and left-handed circularly polarized waves (LCP), respectively. The polarization rotation angle θ and its ellipticity angle η are given as followsFigure 3(a) shows the transmission of circularly polarized waves for the bilayered chiral metamaterial. Obviously, t++ is larger than t- -. As aforementioned, the circular polarization coefficient t+- is extremely identical with t-+ at all frequencies, thus no circular asymmetric transmission occurs. However, this metamaterial exhibits strong circular dichroism (RCP-LCP transmission amplitude difference), especially up to 0.60 at the low frequency band. Figure 3(b) shows the azimuth angle and ellipiticity of the transmitted wave. The azimuth angle θ and the ellipticity η are around 17.35° and 35.24° at 203.8 THz due to partial y-to-x polarization conversion. At 259.8 THz, the azimuth angle θ and the ellipticity η are around 75.91° and 12.53° due to high x-to-y polarization conversion, therefore the transmitted wave is nearly linearly polarized in the vicinity.Fig. 3 (a) Calculated transmission of circularly polarized waves. (b) Polarization rotation azimuth angle θ and ellipticity η of the transmitted wave.
In order to observe the mutual polarization conversion and asymmetric transmission, we have analyzed the electromagnetic wave evolution when propagating through the chiral metamaterial at about 203.8 and 259.8 THz. Figure 4 shows an electric field distribution for an x-polarized wave passing through the slab along the forward and backward directions. In Fig. 4(a), an x-polarized wave along the –z direction cannot pass through the metamaterial slab. However, the x-polarized wave incidents along the z direction at about 203.8 THz [Fig. 4(c)], the fundamental electromagnetic resonance can be excited with a strong electromagnetic wave being coupled into the slab, and then the near-field coupling between the first and second layers results in an obvious transmitted wave, but the polarization direction has been rotated. In contrast, with an x-polarized wave along the z direction at 259.8 THz [Fig. 4(d)], the metamaterial cannot be well excited due to its orientation. Meanwhile, x-polarized wave along the -z direction at 259.8 THz can be converted to its cross-polarization in Fig. 4(b). Therefore, the optical chiral metamaterial can achieve a dual-band polarization conversion for two orthogonal linearly polarized waves.
Fig. 4 The resonant modes in the bilayered chiral metamaterial. Simulated electric field distributions at 203.8 THz (a) and 259.8 THz (b) for an x-polarized wave incident along the forward direction. Simulated electric field distributions at 203.8 THz (c) and 259.8 THz (d) for an x-polarized wave incident along the backward direction.
4. Parameter study and interpretation
Next, we also consider how the geometric parameters affect the transmission coefficients. In Fig. 5, when the gap size b increases from 60nm to 90nm, the capacitance decreases and thus the resonant frequencies of txy and tyx undergo a blueshift. While p increases from 380nm to 410nm, the resonant frequencies of txy and tyx undergo a redshift.
Fig. 5 Calculated transmission coefficients of the bilayered chiral metamaterial for (a) and (b) different gap sizes b and (c) and (d) periods p.
The coupling strength between two layers that is proportional to the thickness of the dielectric layer is an important factor to modulate mutual polarization conversion and dual-band asymmetric transmission. In Fig. 6, when h increases from 30 to 60 nm, the resonant frequency of txy has a much larger redshift than that of tyx. But when the thickness changes, the amplitude of txy reaches a maximum of 0.56 at around 204 THz for an optimal thickness while the amplitude of tyx remains unchanged. The coupling strength provides a convenient way to differently manipulate two polarization conversions, thus asymmetric transmission. These calculated transmission coefficients show that the resonant frequencies can be tuned by varying the geometric parameters.
Fig. 6 Calculated transmission coefficients of the bilayered chiral metamaterial for different thicknesses h.
To analyze the physical origin of the dual-band AT effect, we decompose the chiral optical metamaterial into two parts: concentric and eccentric C-shaped dimers shown in Figs. 7(a) and 7(c). Figures 7(b) and 7(d) show the simulated transmission spectra of the two split components for the forward propagation. Obviously, the concentric C-shaped dimer leads to the x-to-y polarization conversion (tyx) and weak y-to-x polarization conversion (txy) shown in Fig. 7(b), which is similar to the results in [33]. The strong y-to-x polarization conversion occurs in the eccentric C-shaped dimer, much larger than the x-to-y polarization conversion in the frequency range we consider. When two different dimers are integrated into the proposed chiral metamaterial, the x-to-y polarization conversion peak at about 180THz is slightly suppressed and the other peak at about 250THz is almost kept with a weak blueshift due to the coupling effect, while the y-to-x polarization conversion peak has a large redshift of nearly 35THz and meanwhile the polarization conversion at about 300THz is almost suppressed. The y-to-x polarization conversion requires the lateral offset between the front and back C-shaped layers as well as the rotation with respect to each other. Therefore, the x-to-y and y-to-x polarization conversions in the original bilayered chiral metamaterial are attributed to the concentric and eccentric C-shaped dimers, respectively.
Fig. 7 Simulated transmission spectra of the deforming bilayered chiral metamaterial. The bilayered chiral metamaterials can be decomposed into two parts: (a) concentric and (c) eccentric C-shaped dimers. The star marks indicate resonant modes that contribute to the polarization conversions in the proposed bilayered chiral metamaterial.
In order to verify the discussion of the mode contribution above, we present current distributions of the concentric and eccentric C-shaped dimers and the whole bilayered chiral metamaterial at the polarization conversion peaks shown in Fig. 8. Comparing Fig. 8(a) with Fig. 8(c), the resonant mode distribution of the concentric C-shaped dimer is identical to that of the bilayered chiral metamaterial at 259.8 THz. Remarkably, the resonant mode distribution of the eccentric C-shaped dimer is almost the same as that of the bilayered chiral metamaterial at 203.8 THz shown in Figs. 8(b) and 8(d). As a result, the coupling effects in the concentric and eccentric C-shaped dimers result in the x-to-y and y-to-x polarization conversions. When the x-polarized wave is incident onto the front layer in Fig. 8(c), the magnetic resonance can be excited with a strong current. Most of the electromagnetic wave is coupled into the slab. The similar current is observed along the other direction on the back layer. Then the transmitted wave will show x-to-y polarization conversion. The similar phenomenon is also observed when the y-polarized wave is incident at 203.8 THz. Consequently, the metamaterial can reveal the mutual polarization conversion and thus realize a dual-band asymmetric transmission for linearly polarized waves in the infrared.
Fig. 8 Current distributions of the resonant modes at the polarization conversion peaks for forward propagation. (a) and (b) Simulated current distributions of the concentric and eccentric C-shaped dimers at 244.5 and 238.3 THz for x- and y-polarized incident waves, respectively. (c) and (d) Simulated current distributions of the bilayered chiral metamaterial at 259.8 and 203.8 THz for x- and y-polarized incident waves, respectively. The color and arrow indicate the current density.
5. Conclusions
In summary, a mutual polarization conversion and dual-band asymmetric transmission for linearly polarized waves in the optical frequency have been demonstrated in a chiral metamaterials. The chiral metamaterial is constructed by two separate layers of connected I-shape resonators with a twist angle of 90°. The simulated results show that the metamaterial can realize a dual-band polarization conversion for linearly polarized waves in the infrared. The resonant frequencies of polarization conversions can be tuned by varying geometric parameters. The field distributions of the resonant modes verify that the x-to-y and y-to-x polarization conversions in the original bilayered chiral metamaterial are attributed to the concentric and eccentric C-shaped dimers, respectively. We believe that our findings are beneficial in designing polarization controlled devices at infrared frequencies.
Acknowledgments
The authors acknowledge financial support by the National Science Foundation of China under Grants No. 61201083 and U1231201, in part by the China Postdoctoral Science Foundation under Grants No. 2012M511171 and 2013T60487, the Special Foundation for Harbin Young Scientists under Grant No. 2012RFLXG030, the Fundamental Research Funds for the Central Universities, and the 111 Project under Grant No. B13015.
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